The Shapley Value, Proper Shapley Value, and Sharing Rules for Cooperative Ventures

Tinbergen Institute Discussion Paper 2018-089/II

18 Pages Posted: 10 Dec 2018

See all articles by Rene van den Brink

Rene van den Brink

Vrije Universiteit Amsterdam, School of Business and Economics

Rene Levinsky

Charles University in Prague - CERGE-EI (Center for Economic Research and Graduate Education - Economics Institute)

Miroslav Zeleny

Charles University in Prague - Faculty of Mathematics and Physics

Date Written: November 16, 2018

Abstract

Moulin (1987) studies the equal and proportional sharing rule for a special class of cooperative games that he calls joint venture games. Proportionality is an important principle in allocation problems. Besides some special cases, it is not obvious how proportionality should be applied in cooperative TU-games. Such special cases, where proportionality is obvious, are inessential games and cooperative joint venture games. In this paper, we discuss an explicit axiom that shows that proper Shapley values can be seen as an appropriate way to express proportionality in value allocation in cooperative TU-games. We characterize positive proper Shapley values by affine invariance and an axiom that requires proportional allocation according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games, characterize the positive part of the Shapley value among the single-valued solutions.

Keywords: Equity principle, Cooperative venture game, Shapley value, proper Shapley value

JEL Classification: C71

Suggested Citation

van den Brink, Rene and Levinsky, Rene and Zeleny, Miroslav, The Shapley Value, Proper Shapley Value, and Sharing Rules for Cooperative Ventures (November 16, 2018). Tinbergen Institute Discussion Paper 2018-089/II, Available at SSRN: https://ssrn.com/abstract=3285856 or http://dx.doi.org/10.2139/ssrn.3285856

Rene Van den Brink (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Rene Levinsky

Charles University in Prague - CERGE-EI (Center for Economic Research and Graduate Education - Economics Institute) ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

Miroslav Zeleny

Charles University in Prague - Faculty of Mathematics and Physics ( email )

Sokolovska 83
Prague, 186 75
Czech Republic

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